Question

# A lift is tied with thick iron wire and its mass is $$1000 kg$$. If the maximum acceleration of the lift is $$1.2 ms$$$$^{-2}$$ and the maximum stress of the wire is $$1.4$$ x $$10$$$$^{8}$$ Nm$$^{-2}$$, what should be the minimum diameter of the wire ?

A
102 m
B
104 m
C
106 m
D
0.5 x 102 m

Solution

## The correct option is A 10$$^{-2}$$ m$$Stress \times area = M (g + 1.2)$$$$1.4 \times 10^{8} \times \dfrac{\pi}{4}d^2 = 1000(11)$$$${d^{2}} = \dfrac{1000 (11)\times 4}{\pi \times 1.4 \times 10^{8}}$$$$d = \sqrt{\dfrac{4 \times 1000 (11)}{\pi \times 1.4 \times 10^{8}}}$$$$d=\sqrt{\dfrac{10^4}{10^8}}$$$$= 10^{-2}m$$Physics

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